#### Solved Examples and Worksheet for Transformations-Translations

Q1Translate point A(-3, 2) right 4 units. What are the coordinates of its image A'?

A. (-3, -2)
B. (-1, 2)
C. (0, 3)
D. (1, 2)

Step: 1
Count to the right 4 units from point A(-3, 2).
Step: 2
Graph A'.
Step: 3
The coordinates of A' are (1, 2).
Correct Answer is :   (1, 2)
Q2A point P (x, y) is translated 3 units left and 2 units down. Identify a rule for the translation of P.

A. (x, y) → (3, 2)
B. (x, y) → (x + 3, y + 2)
C. (x, y) → (x - 3, y - 2)
D. None of the above

Step: 1
The x and y coordinates of its image P′ become (x - 3) and (y - 2), respectively.
[The point P (x, y) is moved 3 units to left and 2 units down.]
Step: 2
So, the rule for the translation is (x, y) → (x - 3, y - 2).
Correct Answer is :   (x, y) → (x - 3, y - 2)
Q3Identify a rule for the translation, P (5, 5) P′(- 2, 9).
A. (x, y) (7, 4)
B. (x, y) (x + 7, y - 4)
C. (x, y) (x - 7, y + 4)
D. None of the above

Step: 1
The x-coordinate of the image P′ is negative.
Step: 2
So, the point P has been translated to the left.
Step: 3
Number of units, it has been translated left = 5 - (- 2) = 7 units
Step: 4
The y-coordinate of the image P′ is greater than that of the point P.
Step: 5
So, the point P has been translated up.
Step: 6
Number of units, it has been translated up = 9 - 5 = 4 units
Step: 7
So, the rule for the translation is (x, y) (x - 7, y + 4).
Correct Answer is :   (x, y) (x - 7, y + 4)
Q4The coordinates of a point are (- 2, 3) and they are moved to coordinates (2, 3). Identify the steps that can be used for the translation.
A. Move 4 units left.
B. Move 2 units right.
C. Move 4 units right.
D. none of these

Step: 1
The coordinates before translation and after translation are (- 2, 3) and (2, 3).
Step: 2
The x-coordinate after translation is greater than that before translation but the y-coordinate is not changed. So, the translation is towards right.
Step: 3
Translation = 2 - (- 2) = 2 + 2 = 4 units right.
Step: 4
So, move 4 units right from (- 2, 3) to reach (2, 3).
Correct Answer is :   Move 4 units right.
Q5The coordinates of a line segment are (7, 6) and (3, -8). What are the new coordinates of the line segment, if the translation is done to 7 units left?

A. (0, -6) and (-4, -8)
B. (0, 6) and (-4, -8)
C. (0, 6) and (-4, 8)
D. None of the above

Step: 1
The coordinates of the line segment are (7, 6) and (3, -8).
Step: 2
The translation is done by 7 units left.
Step: 3
Since, the translation is done to left, the y-coordinate does not change.
Step: 4
7 - 7 = 0 and 3 - 7 = -4.
[x-coordinates of each end point gets reduced by 7.]
Step: 5
The new coordinates of the line segment are (0, 6) and (-4, -8).
Correct Answer is :   (0, 6) and (-4, -8)
Q6Translate the point T(3, 4), 2 units right, 5 units up , and then 2 units left and 1 unit down. What are the coordinates of the translated image?
A. (3, - 8)
B. (2, 8)
C. (3, 8)
D. none of these

Step: 1
After the first translation, 2 units right and 5 units up, the x-coordinate becomes 3 + 2 = 5 and y-coordinate becomes 4 + 5 = 9 units.
Step: 2
The coordinates after the first translation is (5, 9).
Step: 3
Again the image is translated, 2 units left and 1 unit down, the x-coordinate becomes 5 - 2 = 3 and y-coordinate becomes 9 -1 = 8.
Step: 4
The coordinates of the point after translation is (3, 8).
Correct Answer is :   (3, 8)
Q7Translate the point D(4, 5) to coordinates D′(9, 5). Identify the steps that can be used for the translation.

A. Move 5 units left.
B. Move 5 units right.
C. Move 5 units up.
D. none of these

Step: 1
The two points are (4, 5) and (9, 5).
Step: 2
As the y-coordinate is not changing and the x-coordinate is positive and increasing, the translation is towards right.
Step: 3
The translation of the point is 9 - 4 = 5 units to the right.
Step: 4
So, to translate the point D(4, 5), to coordinates D′(9, 5), move 5 units right.
Correct Answer is :   Move 5 units right.
Q8What are the coordinates of the point P, after it is translated 3 units to the right?

A. (3, - 1)
B. (- 1, 3)
C. (- 1, 2)
D. (1, -3)

Step: 1
The point P is at (- 4, 2).
[From the coordinate plane.]
Step: 2
When the point is translated 3 units to the right the x-coordinate changes, but the y-coordinate remains the same.
Step: 3
After translation the x-coordinate becomes - 4 + 3 = - 1
[As the point is translated to the right.]
Step: 4
The new coordinates of the point P after translation is (- 1, 2)
Correct Answer is :   (- 1, 2)
Q9Find the horizontal change for the translation K (14, 1) K′ (4, 2).

A. 10 units up
B. 10 units down
C. 10 units to the right
D. 10 units to the left

Step: 1
The horizontal change is the change in x-coordinate.
Step: 2
The horizontal change is 10.
Step: 3
Since the x-coordinate of the point K' is less than the x-coordinate of the point K, the horizontal translation is 10 units to the left from the point K.
Correct Answer is :   10 units to the left
Q10Translate the point C(- 2, 2) down 3 units and right 6 units. What are the coordinates of its image C′?

A. (- 1, 4)
B. (4, 1)
C. (4, - 1)
D. (- 4, 1)

Step: 1
When (- 2, 2) is translated down 3 units, the y-coordinate becomes - 1, but the x-coordinate remains same.
Step: 2
After translating (- 2, - 1) to 6 units right, the x-coordinate of the point becomes 4, but the y-coordinate remains same.
Step: 3
So, the coordinates of the new point C′ are (4, - 1).
Correct Answer is :   (4, - 1)
Q11Translate the point O(0, 0)down 2 units and right 5 units. What are the coordinates of its image B′?

A. (5, - 2)
B. (- 2, 0)
C. (- 2, 5)
D. (2, 0)

Step: 1
Plot the point O (0, 0).
Step: 2
Count down 2 units and right 5 units from the point O.
Step: 3
Graph O′.
Step: 4
The coordinates of the image O′ are (5, - 2).
Correct Answer is :   (5, - 2)
Q12Write a rule for the translation, P (8, 7) P′(- 3, 13).

A. (x, y) (x + 11, y - 6)
B. (x, y) (11, 6)
C. (x, y) (x - 11, y + 6)
D. None of the above

Step: 1
The x-coordinate of the image P′ is negative.
Step: 2
So, the point P has been translated to the left.
Step: 3
Number of units, it has been translated left = 8 - (- 3) = 11 units
Step: 4
The y-coordinate of the image P′ is greater than that of the point P.
Step: 5
So, the point P has been translated up.
Step: 6
Number of units it has been translated up = 13 - 7 = 6 units
Step: 7
So, the rule for the translation is (x, y) (x - 11, y + 6).
Correct Answer is :   (x, y) (x - 11, y + 6)
Q13Which figure do you think you would get if you slide (translate) figure (A)?

A. Figure 3
B. Figure 2
C. Figure 1
D. Figure 1 and Figure 2

Step: 1
A transformation in which every point of the figure moves the same distance and in the same direction is called translation or sliding.
Step: 2
Among the 3 figures, Figure 1 represents the slide of the figure(A).
[Figure 1 is 2 units up and 3 units to the right of figure (A).]
Correct Answer is :   Figure 1
Q14Translate the point B (3, 5) right 3 units and up 5 units. What are the coordinates of the image of point B?

A. (- 5, 8)
B. (4, 8)
C. (8, 12)
D. (6, 10)

Step: 1
Plot the point B (3, 5).
Step: 2
Count 3 units right and 5 units up from the point B.
Step: 3
Graph the points.
Step: 4
Therefore, the coordinates of the image of point B = (6, 10 )
Correct Answer is :   (6, 10)
Q15Translate the point T (4, 6), 3 units right, 7 units up and then 2 units left and 1 unit down. What are the coordinates of the translated image?
A. (5, -12)
B. (5, 12)
C. (4, 12)
D. None of the above

Step: 1
After the first translation, 3 units right and 7 units up, the x-coordinate becomes 4 + 3 = 7 and y-coordinate becomes 6 + 7 = 13 units.
Step: 2
The coordinates after the first translation is (7, 13).
Step: 3
Again the image is translated 2 units left and 1 unit down, the x-coordinate becomes 7 - 2 = 5 and y-coordinate becomes 13 -1 = 12.
Step: 4
The coordinates of the point after translation is (5, 12).
Correct Answer is :   (5, 12)